一种新的洪水频率分析方法研究

为解决采用参数法做洪水频率分析时的线型限制问题,同时避免非参数统计法计算过程中复杂的核函数选取问题,提出一种新的洪水频率分析手段,即基于概率密度演化法来推求洪水频率值。首先通过对概率密度演化法的介绍,给出了年最大洪峰流量联合概率密度函数模型;其次利用具有方向自适应性质的单边差分格式对模型进行数值求解,并对求解结果进行积分,得到洪峰流量概率密度函数值;最终,通过三次样条插值及梯形法由洪峰流量概率密度函数值推求洪峰流量频率值。分别以台湾石门水库及黑龙江省嫩江下游的大赉水文站为例,对其洪水频率进行分析。研究结果表明,同实际工程计算中经常应用的参数洪水频率分析方法相比,采用基于概率密度演化法得到的洪水频率曲线能更好地拟合经验频率点据,是一种有效的水文频率分析方法。

Study on a new method for flood frequency analysis

In order to solve the problem of linear limitation for flood frequency analysis in parametric method and avoid the complex process for choosing the kernel function in nonparametric method, a new flood frequency analysis method based on probability density evolution method is proposed for calculating the flood frequency value. Firstly, a joint probability density function model of annual maximum peak discharge is established based on the introduction of probability density evolution method. Secondly,the one-sided difference scheme which has the characteristic of direction adaptive is adopted to solve the model, and then, the numerical results of the model are integrated to get the probability density function of peak discharge. Finally, the probability density function of peak discharge is used to deduce the frequency value of peak discharge via the cubic spline interpolation and trapezoid method. Taking the Shimen Dam in Taiwan and the Dalai hydrologic station located at the downstream of Nen River in Heilongjiang Province as examples, the flood frequency of them are analyzed. The results show that, the flood frequency curve agrees better with the empirical frequency plots by using the probability density evolution method than the curve fitting method that is widely used. And the method based on probability density evolution method is an effective way for hydrologic frequency analysis.